PSLE
The number of boys and girls taking part in a contest are in the ratio 3 : 2. These students are put into two groups. 20% of the boys and 60% of the girls are in Group L. The rest of the students are in Group M.

1. What is the ratio of the number of students in Group M to Group L? Give your answer in the simplest form.
2. The number of girls in Group L is more than 70. What is the smallest possible total number of students taking part in the contest?

Boys		Girls
30 u		20 u
Group L	Group M	Group L	Group M
6 u	24 u	12 u	8 u

(a)
Boys : Girls
3 : 2
30 : 20

Number of boys in Group L
= 20% x 30 u
= ²⁰₁₀₀ x 30 u
= 6 u

Number of boys in Group M
= 30 u - 6 u
= 24 u

Number of girls in Group L
= 60% x 20 u
= ⁶⁰₁₀₀ x 20 u
= 12 u

Number of girls in Group M
= 20 u - 12 u
= 8 u

Group L : Group M
24 + 8 : 6 + 12 
32 : 18 _(÷2)
16 : 9

(b)
Number of girls in Group L = 12 u

Since the number of girls in Group L is 12 u, it must be multiple of 12.

Number of sets of 12
= 70 ÷ 12
= 5 r 10

Since the number of girls in Group L is more than 70, the number of sets must be 1 more than 5.

1 u = 5 + 1 = 6

Smallest possible number of students
= 30 u + 20 u
= 50 u
= 50 x 6
= 300

Answer(s): (a) 16 : 9; (b) 300